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An Irregular Mind: Szemerédi is 70 - download pdf or read online

By Noga Alon (auth.), Imre Bárány, József Solymosi, Gábor Sági (eds.)

ISBN-10: 3642144438

ISBN-13: 9783642144431

Szemerédi's effect on contemporary arithmetic, specifically in combinatorics, additive quantity thought, and theoretical laptop technology, is gigantic. This quantity is a party of Szemerédi's achievements and character, at the get together of his 70th birthday. It exemplifies his remarkable imaginative and prescient and exact frame of mind. a couple of colleagues and pals, all most sensible specialists of their fields, have contributed their most recent examine papers to this quantity. the themes comprise extension and purposes of the regularity lemma, the lifestyles of k-term mathematics progressions in a variety of subsets of the integers, extremal difficulties in hypergraphs conception, and random graphs, them all appealing, Szemerédi style arithmetic. It additionally comprises released bills of the 1st , very unique and hugely winning Polymath initiatives, one led by way of Tim Gowers and the opposite through Terry Tao.

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Extra resources for An Irregular Mind: Szemerédi is 70

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The reflection off the boundary is elastic, meaning the familiar law of reflection: the angle of incidence equals the angle of reflection. ). , the starting point of the billiard path and the initial direction, uniquely determine an infinite piecewise linear billiard path x( t) = (Xl (t), X2 (t)), 0 < t < 00 in the unit square. The law of reflection implies that there are at most four different directions along the billiard path (the initial direction is preserved modulo 7f/2, which is one-fourth of the whole angle 27f).

Cannot be all 0(1) . 1) even for the simplest families of subsets. (4) As I already said above, we can make the vague term "1 - c part of all billard paths" in Theorem 1 precise by using the product measure on the set of all initial conditions of the billiard paths. Since the initial condition consists of a starting point y E [0, 1)2 and an initial direction (angle) e E [0,27r) , the natural measure here is simply the product of the two-dimensional Lebesgue measure on the unit square and the normalized one-dimensional Lebesgue measure .

Area (A) I < lea Jarea (A) (1- area (A)) . )log2 T ·log2log2 T . Remarks. (1) Note that Theorem 1 remains true if "billiard path" is replaced with "torus line". Indeed , in view of the trick of unfolding, the two concepts are basically the same. , Theorems 2 and 3 below). 1). 1) is nearly sharp in the following strong sense. 1) is still unavoidable , we cannot have 0(1) instead (to be explained below). This shows that in Theorem 1 the complexity of the test set A c [0, 1)2 is basically irrelevant.

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An Irregular Mind: Szemerédi is 70 by Noga Alon (auth.), Imre Bárány, József Solymosi, Gábor Sági (eds.)


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